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We, fourth-year students of the educational program “Computational Sciences and Statistics” at the Faculty of Mechanics and Mathematics of 91��ý Kazakh National University, completed an industrial internship that became an important and memorable stage in our professional development. This internship was organized under the supervision of Academician of the National Academy of Engineering of the Republic of Kazakhstan and the National Academy of Sciences of the Republic of Kazakhstan, Doctor of Physical and Mathematical Sciences, Professor Nurlan Mukanovich Temirbekov. During the internship, we not only improved our professional skills but also had the opportunity to establish direct communication with a world-class scientist. One of the most significant highlights of the internship was the lectures and regular scientific meetings with Doctor of Physical and Mathematical Sciences, Professor Petr Nikolaevich Vabishchevich. We met twice a week in an online format, discussed complex theoretical issues, and jointly analyzed important problems related to mathematical modeling and computational methods.

P.N. Vabishchevich is one of the prominent representatives of modern computational mathematics. He is a leading scientist who has achieved fundamental results in the numerical solution of differential equations, numerical methods including the finite element method, as well as mathematical modeling. His scientific works cover the stability of difference schemes, operator-splitting methods, finite element methods, and the modeling of complex systems, and are highly regarded by the international scientific community. Professor Vabishchevich is widely known for his scientific contributions: he is the author of more than 100 scientific articles, as well as over 20 monographs and textbooks. These works are widely used in higher education institutions and serve as an important scientific foundation for young researchers. In addition, he makes a significant contribution to leading scientific projects and training young scientists. Under his supervision, numerous research works have been successfully defended, and a scientific school has been established.

It should be especially noted that a decisive influence on the formation of the scientist was exerted by the outstanding mathematician, Doctor of Physical and Mathematical Sciences, Professor, Academician of the USSR Academy of Sciences Alexander Andreevich Samarskii, who was the scientific advisor of P.N. Vabishchevich. The scientific school founded by him not only gave a powerful impetus to the development of computational mathematics but also established the fundamental theoretical foundations of numerical methods. This scientific school remains relevant today and is recognized as one of the leading directions in modern computational science. Professor P.N. Vabishchevich, as a worthy successor of this school, has successfully developed its ideas, elevated them to a qualitatively new level, and effectively adapted them to solving modern complex mathematical problems.

During the lectures, we were able to observe not only the depth of the scientist’s theoretical knowledge but also his ability to explain complex concepts in a clear and accessible manner. Using concrete examples, he revealed the essence of operator-splitting methods and their role in improving computational efficiency, demonstrating the close connection between theory and practice.

During the industrial internship, we thoroughly mastered modern approaches to mathematical modeling and numerical methods. A special focus was placed on the finite element method as a fundamental tool for analysis and computation. This method is considered a universal approach for solving differential equations in complex geometrical domains, where its core idea lies in dividing the domain into small elements and constructing an approximate solution on each of them. Using the finite element method, we learned to numerically analyze integral and differential equations and mastered algorithms for efficiently solving complex problems. In practice, we became convinced that this method makes it possible to adapt theoretical models to real-world problems and improve the accuracy and stability of computations.

As an integral part of the scientific process, we actively used modern computational technologies. In particular, using the FEniCS platform, we implemented mathematical problems based on the finite element method, and with the help of Streamlit, we presented research results in a clear and interactive form. In addition, we prepared scientific presentations on modern software tools such as Matplotlib, NumPy, Streamlit, SciPy, and Gmsh, and presented them to Professor P.N. Vabishchevich. These activities allowed us to elevate our programming and scientific analysis skills to a new level.

Direct interaction with a scientist of such a high level became a powerful source of motivation for us. We deeply realized that computational mathematics is not only a theoretical discipline but also an important field widely applied in geophysics, engineering, and the modeling of natural processes.

In conclusion, we would like to emphasize that this industrial internship was not merely a part of the educational process but an important stage that expanded our scientific worldview. This experience provided a strong impetus for our professional and academic development and strengthened our interest in pursuing a scientific career in the future. We also hope that such internships will continue in the future, providing students with opportunities to effectively acquire research skills. The lectures and scientific meetings with Professor P.N. Vabishchevich will remain an unforgettable experience for us.